Four children and six women were among those who died after the small vessel sank in the Meghna river, about 40km southeast of the capital, Dhaka, officials said on Monday.
Witnesses said the ferry was carrying more than 100 people going home for Eid-ul-Fitr, which marks the end of Ramadan, the Muslim month of fasting.
Rescue workers are attempting find 35 other people who remain missing and also salvage the ferry which is about 20 metres under water.
"The ferry MV Baba Shahparan sank immediately after the collision," an official of Bangladesh Water Transport Authority said.
Half of those on board were either rescued or managed to swim to safety.
Ferry accidents, often blamed on lax rules and unsafe navigation, are common in the delta nation of 144 million people.
Last year, more than 300 people died in such incidents.
About 20,000 cargo and passenger vessels operate in the South Asian nation, about half of which fail to meet basic safety standards or illegally take on passengers, according to an independent study last year.
More than 2,000 designated ferries carry about 100,000 passengers a day across the country's 7,000 km river routes, the study said.